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Math Problems
Algebra 1
Experimental probability
The Venn diagram below shows information about the number of items in sets
A
\mathrm{A}
A
and
B
\mathrm{B}
B
. There are
23
23
23
items in total.
\newline
What is the probability that an item chosen at random is in
A
′
∩
B
′
\mathrm{A}^{\prime} \cap \mathrm{B}^{\prime}
A
′
∩
B
′
? Give your answer as a fraction in its simplest form.
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Jace mixed
17
17
17
gallons of two fruit drink brands. Brand A contains
14
%
14 \%
14%
fruit juice and Brand B contains
48
%
48 \%
48%
fruit juice. If the resulting mixture contains
30
%
30 \%
30%
fruit juice, how many gallons of each should he use?
\newline
Let
\qquad
=
=
=
\qquad
and Let
\qquad
=
=
=
\qquad
\newline
(
13
13
13
)
\newline
(
14
14
14
)
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(
9
9
9
) Jace mixed
17
17
17
gallons of two fruit drink brands. Brand A contains
14
%
14 \%
14%
fruit juice and Brand
B
B
B
contains
48
%
48 \%
48%
fruit juice. If the resulting mixture contains
30
%
30 \%
30%
fruit juice, how many gallons of each should he use?
\newline
Let
\qquad
=
=
=
\qquad
and Let
\qquad
□
+
L
=
□
\square+L=\square
□
+
L
=
□
\newline
(
13
13
13
) (
14
14
14
)
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Jayden and his mom have been saving recycling items for months, and today they traded them in. They made
$
42
\$42
$42
on cans,
$
19
\$19
$19
on glass bottles, and
$
32
\$32
$32
on plastic bottles. Jayden estimates that they made around
$
140
\$140
$140
. Is that a good estimate?
\newline
Choices:
\newline
(A) Yes.
\newline
(B) No, it is much too high.
\newline
(C) No, it is much too low.
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Six teachers, seventy-eight students, and ten parents are boarding buses for a school field trip. Each bus can carry
32
32
32
passengers.
\newline
If the passengers board each bus until it is full, how many passengers (
p
p
p
) will be on the bus that is not full?
\newline
There will be
□
\square
□
passengers on the bus that is not full.
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Childhood obesity: A national health survey weighed a sample of
546
546
546
boys aged
6
6
6
−
11
-11
−
11
and found that
74
74
74
of thern were overweight. They weighed a sample of
455
455
455
girls aged
6
6
6
−
11
-11
−
11
and found that
75
75
75
of them were overwight. Can you conclude that the proportion of boys who are overweight is less than the proportion of girls who are overweight? Let
p
1
p_{1}
p
1
denote the proportion of boys who are overweight and let
p
2
p_{2}
p
2
denote the proportion of girls who are overweight. Use the
α
=
0.10
\alpha=0.10
α
=
0.10
level of significance and the
P
P
P
-value method with the Ti-b
4
4
4
Plus calculator:
\newline
Part:
0
/
4
0 / 4
0/4
\newline
Part
1
1
1
of
4
4
4
\newline
State the appropriate null and alternate hypotheses.
\newline
H
0
:
H_{0}:
H
0
:
□
\square
□
\newline
H
1
:
□
H_{1}: \square
H
1
:
□
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By dinnertime, Bella had finished
7
8
\frac{7}{8}
8
7
of the questions from her history homework. Her friend, Shivani, had finished
1
4
\frac{1}{4}
4
1
of the questions from her homework. Who had finished a greater fraction of her questions?
\newline
Choices:
\newline
(A) Bella
\newline
(B) Shivani
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Javier read a report that said the probability that a randomly selected American is left-handed is
.
H
e
w
a
s
c
u
r
i
o
u
s
h
o
w
m
a
n
y
l
e
f
t
−
h
a
n
d
e
d
s
t
u
d
e
n
t
s
t
o
e
x
p
e
c
t
i
n
a
c
l
a
s
s
o
f
. He was curious how many left-handed students to expect in a class of
.
He
w
a
sc
u
r
i
o
u
s
h
o
w
man
y
l
e
f
t
−
han
d
e
d
s
t
u
d
e
n
t
s
t
oe
x
p
ec
t
ina
c
l
a
sso
f
students. He simulated
c
l
a
s
s
e
s
o
f
classes of
c
l
a
sseso
f
students where each student selected had a
probability of being left-handed. Javier counted how many left-handed students were in each simulated class. Here are his results:
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Ronnie and Roxanne went to the track after school. Ronnie ran
6
6
6
laps in
15
15
15
minutes. Roxanne ran
9
9
9
laps in
20
20
20
minutes. Who ran faster?
\newline
Choices:
\newline
(A)Ronnie
\newline
(B)Roxanne
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13
13
13
. In a perfectly competitive labor market, an increase in an effective minimum wage will result in
\newline
(A) an increase in the supply of workers
\newline
(B) a decrease in the supply of workers
\newline
(C) a decrease in the demand for workers
\newline
(D) more workers being hired
\newline
(E) fewer workers being hired
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The chips shown are placed in a bag and drawn at random, one by one, without replacement.
\newline
What is the probability that the first two chips drawn are both red?
\newline
The probability is
□
\square
□
\newline
(Simplify your answer.)
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A shipment of sugar fills
10
10
10
containers. If each container holds
2
3
4
2 \frac{3}{4}
2
4
3
tons of sugar, what is the amount of sugar in the entire shipment?
\newline
Write your answer as a mixed number in simplest form.
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Katie is measured every year at her annual checkup. When she was
11
11
11
, she was
57
57
57
inches tall. When she was
12
12
12
, she was
59
59
59
inches tall. She just turned
13
13
13
, and now she is
63
63
63
inches tall. Is the relationship between Katie's age and her height a linear relationship?
\newline
Choices:
\newline
(A)yes
\newline
(B)no
\newline
Now, justify your answer.
\newline
Choices:
\newline
(A)Katie's height increased by the same amount each year.
\newline
(B)Katie's height increased by a different amount each year.
\newline
(C)Katie got taller every year.
\newline
(D)Katie's age increased by
1
1
1
every year.
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Madison started hiking at an elevation of
4
4
4
meters above sea level. She hiked up at a rate of
3
3
3
meters per minute. The graph below represents the relationship between the number of minutes and the elevation.
1
1
1
) What is the slope of the line? slope
=
=
=
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The cafeteria director at Great Minds School wants to know what percent of the students would choose vegetarian entrees if they were available.
\newline
Which of the following survey methods will allow the director to make a valid conclusion about the percentage of students who would choose vegetarian entrees?
\newline
Choose
1
1
1
answer:
\newline
(A) Sort a list of the students into a random order, then ask the first
35
35
35
students on the list.
\newline
(B) Ask the first
35
35
35
students in line for the cafeteria.
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(a) A certain committee consists of
16
16
16
people. From the committee, a president, a vice-president, a secretary, and a treasurer are to be chosen. In how many ways can these
4
4
4
offices be filled? Assume that a committee member can hold at most one of these offices.
\newline
□
\square
□
\newline
(b) A company has
37
37
37
salespeople. A board member at the company asks for a list of the top
5
5
5
salespeople, ranked in order of effectiveness. How many such rankings are possible?
\newline
□
\square
□
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Suppose we want to choose
6
6
6
letters, without replacement, from
9
9
9
distinct letters.
\newline
(a) If the order of the choices is not relevant, how many ways can this be done?
\newline
□
\square
□
\newline
(b) If the order of the choices is relevant, how many ways can this be done?
\newline
□
\square
□
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A technology company is going to issue new ID codes to its employees. Each code will have two letters, followed by one digit, followed by one letter. The letters
D
,
G
D, G
D
,
G
, and
Z
Z
Z
and the digit
8
8
8
will not be used. So, there are
23
23
23
letters and
9
9
9
digits that will be used. Assume that the letters can be repeated. How many employee ID codes can be generated?
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\begin{tabular}{|c|c|c|c|}
\newline
\hline Question
5
5
5
, & ר & HW Score:
73.89
%
73.89 \%
73.89%
, & \{్ర \\
\newline
\hline Part
3
3
3
of
4
4
4
& & (x) Points:
0
0
0
.
5
5
5
of
1
1
1
& Save \\
\newline
\hline
\newline
\end{tabular}
\newline
A simple random sample of size
n
=
14
n=14
n
=
14
is obtained from a population with
μ
=
69
\mu=69
μ
=
69
and
σ
=
16
\sigma=16
σ
=
16
.
\newline
(a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities involving the sample mean? Assuming that this condition is true, describe the sampling distribution of
x
ˉ
\bar{x}
x
ˉ
.
\newline
(b) Assuming the normal model can be used, determine
P
(
x
ˉ
<
73.4
)
\mathrm{P}(\bar{x}<73.4)
P
(
x
ˉ
<
73.4
)
.
\newline
(c) Assuming the normal model can be used, determine
P
(
x
ˉ
≥
70.7
)
P(\bar{x} \geq 70.7)
P
(
x
ˉ
≥
70.7
)
.
\newline
(a) What must be true regarding the distribution of the population?
\newline
A. Since the sample size is large enough, the population distribution doe need to be normal.
\newline
B. The sampling distribution must be assumed to be normal.
\newline
C. The population must be normally distributed.
\newline
D. The population must be normally distributed and the sample size must be large.
\newline
Assuming the normal model can be used, describe the sampling distribution
x
ˉ
\bar{x}
x
ˉ
. Choose the correct answer below.
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A coin is flipped and a number cube is rolled. The tree diagram below shows the possible outcomes. Use the diagram to answer the questions.
\newline
(a) How many outcomes are there?
\newline
□
\square
□
outcome(s)
\newline
(b) How many outcomes involve rolling a
2
2
2
or a
3
3
3
?
\newline
□
\square
□
outcome(s)
\newline
(c) How many outcomes involve tails and an odd number?
\newline
□
\square
□
outcome(s)
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Shaq tried
18
18
18
free throw attempts playing basketball. He succeeded
0
0
0
times.
\newline
What is the experimental probability of succeeding on his next attempt? Write your answer as a fraction.
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A company that manufactures small canoes has a fixed cost of
$
24
,
000
\$ 24,000
$24
,
000
. It costs
$
40
\$ 40
$40
to produce each canoe. The selling price is
$
160
\$ 160
$160
per canoe. (In solving this exercise, let
x
x
x
represent the number of canoes produced and sold.)
\newline
a. Write the cost function.
\newline
C
(
x
)
=
□
\mathrm{C}(\mathrm{x})=\square
C
(
x
)
=
□
(Type an expression using
x
\mathrm{x}
x
as the variable.)
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Review
:
≡
: \equiv
:≡
\newline
Bookmark
\newline
GRADE
8
8
8
MATHEMATICS - UNIT
3
3
3
/ UNIT
3
3
3
(CALCULATOR) /
6
6
6
OF
10
10
10
\newline
60
%
60 \%
60%
\newline
Quadrilaterals
R
S
T
U
R S T U
RST
U
and
A
B
C
D
A B C D
A
BC
D
are shown on the coordinate plane.
\newline
Listen
\newline
A student says that the quadrilaterals are not similar because they are not the same shape. The student also says that the quadrilaterals are not congruent.
\newline
- Determine whether the student is correct in terms of similarity. Explain your answer.
\newline
- Determine whether the student is correct in terms of congruence. Explain your answer.
\newline
- Use a sequence of transformations as part of your explanations.
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You're having dinner at a restaurant that serves
5
5
5
kinds of pasta (spaghetti, bow ties, fettuccine, ravioli, and macaroni) in
4
4
4
different flavors (tomato sauce, cheese sauce, meat sauce, and olive oil).
\newline
If you randomly pick your kind of pasta and flavor, what is the probability that you'll end up with something other than tomato spaghetti?
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a. Write an equation to represent the nangei. b. Explain how to reason with the hanger to find the value of
x
x
x
. Q. Explain how to reason with the equation to find the value of
x
x
x
. Andre says that
x
x
x
is
7
7
7
because he can move the two
1
1
1
s with the
x
x
x
to the other side. Do you agree with Andre? Explain your reasoning.
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Chinese YMCA Secondary School (Mathematics Paper
1
1
1
)
\newline
16
16
16
. Baguette sold
2
2
2
identical baguettes at the same price. One was sold at a
20
%
20\%
20%
profit and another was sold at a
20
%
20\%
20%
loss. Is there an overall profit or loss? Explain. (
4
4
4
marks)
\newline
let
b
b
b
be the sell of a baguette
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Chinese YMCA Secondary School (Mathematics Paper
1
1
1
)
\newline
16
16
16
. Baguette sold
2
2
2
identical baguettes at the same price. One was sold at a
20
%
20 \%
20%
profit and another was sold at a
20
%
20 \%
20%
loss. Is there an overall profit or loss? Explain. (
4
4
4
marks)
\newline
Let
b
b
b
be the sell, of a baguetie
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On January
1
st
,
2014
1^{\text {st }}, 2014
1
st
,
2014
, approximately
450
450
450
thousand buildings in the United States (US) had solar panels. This number increased by a total of about
180
180
180
thousand over the next
12
12
12
months. Assuming a constant rate of change, approximately how many months after January
1
st
,
2014
1^{\text {st }}, 2014
1
st
,
2014
would
900
900
900
thousand buildings in the US have solar panels?
\newline
□
\square
□
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At Downtown Pizza,
4
4
4
of the last
6
6
6
pizzas sold had pepperoni. What is the experimental probability that the next pizza sold will have pepperoni?
\newline
Simplify your answer and write it as a fraction or whole number.
\newline
P
(
\mathrm{P}(
P
(
pepperoni
)
=
)=
)
=
□
\square
□
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The traditional Australian game of 'Two-Up' involves tossing two coins. Players can bet either on two heads (HH) or two tails (TT). If a head and a tail is thrown (HT or TH), the player continues tossing until either HH or TT results. If
5
5
5
successive tosses result in a
H
\mathrm{H}
H
and
T
\mathrm{T}
T
, all bets loose, and the game is finished.
\newline
Using your table from Question (
3
3
3
), answer the following questions:
\newline
(a) Find the probability that the game finishes on the first toss. Explain your answer.
\newline
(
2
2
2
marks)
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Debbie's Cupcakes recently sold
3
3
3
vanilla cupcakes and
3
3
3
other cupcakes. What is the experimental probability that the next cupcake sold will be a vanilla cupcake? Simplify your answer and write it as a fraction or whole number.
\newline
P
(
vanilla cupcake
)
=
_
_
P(\text{vanilla cupcake}) = \_\_
P
(
vanilla cupcake
)
=
__
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Diane has pulled
2
2
2
green marbles and
10
10
10
other marbles from a large bag. What is the experimental probability that the next marble selected from the bag will be green?
\newline
Simplify your answer and write it as a fraction or whole number.
\newline
P
(
green
)
=
_
_
_
_
P(\text{green}) = \_\_\_\_
P
(
green
)
=
____
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Of the
18
18
18
people who have signed up for a genetics lecture,
8
8
8
have hazel eyes. What is the experimental probability that the next person to sign up will have hazel eyes?
\newline
Simplify your answer and write it as a fraction or whole number.
\newline
P
(
hazel
)
=
_
_
_
_
P(\text{hazel}) = \_\_\_\_
P
(
hazel
)
=
____
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The population of a city decreases by
3
%
3 \%
3%
per year. What should we multiply the current population by to find next year's population in one step?
\newline
Answer:
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Scarlett owns a small business selling ice-cream. She knows that in the last week
49
49
49
customers paid cash,
2
2
2
customers used a debit card, and
4
4
4
customers used a credit card.
\newline
Based on these results, express the probability that the next customer will pay with cash as a fraction in simplest form.
\newline
Answer:
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Aria has a bag that contains strawberry chews, lemon chews, and watermelon chews. She performs an experiment. Aria randomly removes a chew from the bag, records the result, and returns the chew to the bag. Aria performs the experiment
44
44
44
times. The results are shown below:
\newline
A strawberry chew was selected
7
7
7
times.
\newline
A lemon chew was selected
16
16
16
times.
\newline
A watermelon chew was selected
21
21
21
times.
\newline
Based on these results, express the probability that the next chew Aria removes from the bag will be a flavor other than watermelon as a percent to the nearest whole number.
\newline
Answer:
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A box contains
16
16
16
transistors,
4
4
4
of which are defective. If
4
4
4
are selected at random, find the probability of the statements below.
\newline
a. All are defective
\newline
b. None are defective
\newline
a. The probability is
□
\square
□
.
\newline
(Type a fraction. Simplify your answer.)
\newline
b. The probability is
□
\square
□
.
\newline
(Type a fraction. Simplify your answer.)
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tion list
\newline
A group consists of four Democrats and eight Republicans. Three people are selected to attend a conference.
\newline
a. In how many ways can three people be selected from this group of twelve?
\newline
b. In how many ways can three Republicans be selected from the eight Republicans?
\newline
c. Find the probability that the selected group will consist of all Republicans.
\newline
estion
4
4
4
\newline
estion
5
5
5
\newline
a. The number of ways to select three people from the group of twelve is
□
\square
□
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At Donut King,
4
4
4
of the last
16
16
16
donuts sold had sprinkles. What is the experimental probability that the next donut sold will have sprinkles? Simplify your answer and write it as a fraction or whole number.
\newline
P
(
sprinkles
)
=
_
_
_
P(\text{sprinkles}) = \_\_\_
P
(
sprinkles
)
=
___
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An orange-and-green spinner landed on orange
2
2
2
times and on green
18
18
18
times. What is the experimental probability that the next spin will land on orange? Simplify your answer and write it as a fraction or whole number.
\newline
P
(
orange
)
=
_
_
_
P(\text{orange}) = \_\_\_
P
(
orange
)
=
___
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Aubrey's Pie Shop recently sold
6
6
6
cherry pies and
14
14
14
other pies. What is the experimental probability that the next pie sold will be a cherry pie? Simplify your answer and write it as a fraction or whole number.
\newline
P
(
cherry pie
)
=
_
_
_
P(\text{cherry pie}) = \_\_\_
P
(
cherry pie
)
=
___
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Meg surveyed some students at her school about their favorite professional sports. Of the students surveyed,
2
2
2
said football was their favorite sport, while
8
8
8
of the students had other favorite sports. What is the experimental probability that the next student Meg talks to will pick football?
\newline
Simplify your answer and write it as a fraction or whole number.
\newline
P
(
football
)
=
_
_
_
_
P(\text{football}) = \_\_\_\_
P
(
football
)
=
____
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Lillian is sitting on a bench in the mall. She noticed that
3
3
3
out of the last
15
15
15
men who walked by had a beard. What is the experimental probability that the next man to walk by will have a beard?
\newline
Simplify your answer and write it as a fraction or whole number.
\newline
P
(
beard
)
=
_
_
_
_
P(\text{beard}) = \_\_\_\_
P
(
beard
)
=
____
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Brennan's Breakfast Goodies recently sold
20
20
20
muffins, of which
4
4
4
were pumpkin spice muffins. What is the experimental probability that the next muffin sold will be a pumpkin spice muffin? Simplify your answer and write it as a fraction or whole number.
\newline
P
(
pumpkin spice muffin
)
=
_
_
P(\text{pumpkin spice muffin}) = \_\_
P
(
pumpkin spice muffin
)
=
__
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Hometown Donuts recently sold
19
19
19
donuts, of which
6
6
6
were cream-filled donuts. What is the experimental probability that the next donut sold will be a cream-filled donut? Simplify your answer and write it as a fraction or whole number.
\newline
P
(
cream-filled donut
)
=
_
_
P(\text{cream-filled donut}) = \_\_
P
(
cream-filled donut
)
=
__
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At Downtown Dogs,
10
10
10
of the last
15
15
15
customers wanted mustard on their hot dogs. What is the experimental probability that the next customer will want mustard? Simplify your answer and write it as a fraction or whole number.
\newline
P
(
mustard
)
=
_
_
P(\text{mustard}) = \_\_
P
(
mustard
)
=
__
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At City Burger,
4
4
4
of the last
8
8
8
customers wanted cheese on their burgers. What is the experimental probability that the next customer will want cheese on his or her burger? Simplify your answer and write it as a fraction or whole number.
\newline
P
(
cheese
)
=
_
_
P(\text{cheese}) = \_\_
P
(
cheese
)
=
__
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A band played an encore at
2
2
2
of its last
6
6
6
shows. What is the experimental probability that the band will play an encore at its next show? Simplify your answer and write it as a fraction or whole number.
\newline
P
(
encore
)
=
_
_
_
P(\text{encore}) = \_\_\_
P
(
encore
)
=
___
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A florist sold
6
6
6
flower bouquets yesterday, including
3
3
3
daisy bouquets. What is the experimental probability that the next bouquet sold will be a daisy bouquet? Simplify your answer and write it as a fraction or whole number.
\newline
P
(
daisy
)
=
_
_
_
P(\text{daisy}) = \_\_\_
P
(
daisy
)
=
___
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Candice's Cupcakes recently sold
15
15
15
cupcakes, of which
6
6
6
were chocolate cupcakes. What is the experimental probability that the next cupcake sold will be a chocolate cupcake? Simplify your answer and write it as a fraction or whole number.
\newline
P
(
chocolate cupcake
)
=
_
_
P(\text{chocolate cupcake}) = \_\_
P
(
chocolate cupcake
)
=
__
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